Abstract

Let G(V,E) be a graph, and let f:G->R² be a one to one function that produces a layout of a graph G on the plane. We consider the problem of assigning text labels to every edge of the graph such that the quality of the labeling assignment is optimal. This problem has been first encountered in automated cartography and has been refferedto as the Line Feature Label Placement (LFLP) problem. Even though much effort has been devoted over the last 15 years in the area of automated drawing of maps, the Edge Label Placement (ELP) problem has received little attention. In this paper we investigate computational complexity issues of the ELP problem, which have been open up to the present time. Specifically we prove that the ELP problem is NP-Hard.

T. Kato and H. Imai. The NP-completeness of the character placement problem of 2 or 3 degrees of freedom. Record of Joint Conference of Electrical and Electronic Engineers in Kyushu, 1138, 1988. In Japanese.